By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]....By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed state of the excitons is investigated. Our result shows that, the classical field can compensate the energy dissipation of the excitons. Although the decoherence rate of the excitonic Schr?dinger cat state does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the amplitude of the external field as well as the detuning between the field and the transition frequency of the atom.展开更多
We discuss a methodology problem which is crucially important for solving the Sch?dinger equation in terms of the variational method. We present a complete analysis on the application of the hypervirial theorem for ju...We discuss a methodology problem which is crucially important for solving the Sch?dinger equation in terms of the variational method. We present a complete analysis on the application of the hypervirial theorem for judging the quality of the trial wavefunction without invoking the precise solutions.展开更多
We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The rel...We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The relationobtained here emerges very easily from a transformation introduced by Ray [J.R. Ray, Phys. Rev. A26 (1982) 729] andgeneralizes former work of Dodonov et al. [V.V. Dodonov, V.I. Man'ko, and D.E. Nikonov, Phys. Lett. A162 (1992)359.]展开更多
We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find th...We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.展开更多
The interaction of N two-level atoms with both a two-mode cavity field and an external classical pumpingfield, and with the fields being degenerate in frequency, is studied in the regime where the atoms and fields are...The interaction of N two-level atoms with both a two-mode cavity field and an external classical pumpingfield, and with the fields being degenerate in frequency, is studied in the regime where the atoms and fields are highlydetuned. This dispersive interaction can be used to generate a large number of important entangled coherent statesconditional on the initial atomic states and state-selective measurements. A dynamical relation is established betweenthe results for the case with continuous pumping and the case without external driving where the coherent field is putin as the initial condition.展开更多
Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of...Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schr¨odinger(NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.展开更多
The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eig...The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.展开更多
In this article, we apply the Generalized Uncertainty Principle （GUP）, which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this s...In this article, we apply the Generalized Uncertainty Principle （GUP）, which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this system. The generalized Hamiltonian contains two additional terms, which are proportional to ap3 （the result of the maximum momentum assumption） and a2p4 （the result of the minimum length assumption）, where a - 1/MpIc is the GUP parameter. On the basis of the work by Ali et al., we solve the generaiized Schrodinger equation which is extended to include the a2 correction term, and find that the length L of the finite potentiai well must be quantized. Then a generalization to the double-square-well potential is discussed. The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of aolp1 in GUP scenario.展开更多
The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by...The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by the nonlinear Schro¨ dinger equation. At high bending and high nonlinearity, topological trapping is frustrated by the generation of curved wave-breaking. Four-dimensional parallel simulations confirm the theoretical model. This work may contribute to novel devices based on geometrically constrained highly nonlinear dynamics and tests and analogs of fundamental physical theories in curved space.展开更多
文摘By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed state of the excitons is investigated. Our result shows that, the classical field can compensate the energy dissipation of the excitons. Although the decoherence rate of the excitonic Schr?dinger cat state does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the amplitude of the external field as well as the detuning between the field and the transition frequency of the atom.
文摘We discuss a methodology problem which is crucially important for solving the Sch?dinger equation in terms of the variational method. We present a complete analysis on the application of the hypervirial theorem for judging the quality of the trial wavefunction without invoking the precise solutions.
文摘We obtain a new relation between Green's functions of the time-dependent Schrōdinger equation forstationary potentials and Green's functions of the same equation for certain time-dependent potentials. The relationobtained here emerges very easily from a transformation introduced by Ray [J.R. Ray, Phys. Rev. A26 (1982) 729] andgeneralizes former work of Dodonov et al. [V.V. Dodonov, V.I. Man'ko, and D.E. Nikonov, Phys. Lett. A162 (1992)359.]
基金The project supported by the Natural Science Foundation of Yunnan Province under Grant No. 2005A20002M.Acknowledgments We express our sincere thanks to Ke-Zhao Zhou and Bo Xiong for helpful discussions.
文摘We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.
基金The project supported by National Natural Science Foundation of China
文摘The interaction of N two-level atoms with both a two-mode cavity field and an external classical pumpingfield, and with the fields being degenerate in frequency, is studied in the regime where the atoms and fields are highlydetuned. This dispersive interaction can be used to generate a large number of important entangled coherent statesconditional on the initial atomic states and state-selective measurements. A dynamical relation is established betweenthe results for the case with continuous pumping and the case without external driving where the coherent field is putin as the initial condition.
基金Supported by the Research Grants Council contract HKU17200815
文摘Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schr¨odinger(NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.
文摘The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.
基金Supported by National Natural Science Foundation of China under Grant Nos.10865003 and 11464005
文摘In this article, we apply the Generalized Uncertainty Principle （GUP）, which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this system. The generalized Hamiltonian contains two additional terms, which are proportional to ap3 （the result of the maximum momentum assumption） and a2p4 （the result of the minimum length assumption）, where a - 1/MpIc is the GUP parameter. On the basis of the work by Ali et al., we solve the generaiized Schrodinger equation which is extended to include the a2 correction term, and find that the length L of the finite potentiai well must be quantized. Then a generalization to the double-square-well potential is discussed. The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of aolp1 in GUP scenario.
基金the support of a grant from the John Templeton Foundation(58277)support by the European Research Council Grant ERC-POC-2014 Vanguard(664782)
文摘The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by the nonlinear Schro¨ dinger equation. At high bending and high nonlinearity, topological trapping is frustrated by the generation of curved wave-breaking. Four-dimensional parallel simulations confirm the theoretical model. This work may contribute to novel devices based on geometrically constrained highly nonlinear dynamics and tests and analogs of fundamental physical theories in curved space.
